
page = '# Introduction\n' +
    '\n' +
    '定义 \n' +
    '\n' +
    '\n' +
    '$$\n' +
    '\\sum_i a\n' +
    '$$\n' +
    'or\n' +
    '$$\n' +
    '\\mathcal{E}( t)  = t^4 \\cdot   \\Big(  F(\\lambda(t))  -F(\\lambda^\\ast) \\Big)\n' +
    '+   \\Big\\|    t\\cdot      \\dot \\lambda(t) +4  \\cdot \\lambda(t)  -4 \\cdot \\lambda^\\ast\\Big\\|_2^2 ,\\\\\n' +
    '\\frac{d^2\\lambda(t)}{dt^2} + \\frac{5}{t} \\frac{d\\lambda(t)}{dt} + t^2/2 \\cdot  \\nabla F(\\lambda ) = 0\n' +
    '$$\n' +
    '证明证明\n' +
    '$$\n' +
    '\\mathcal{E}( t)  = t^4 \\cdot   \\Big(  F(X(t))  -F(X^\\ast) \\Big)\n' +
    '+   \\Big\\|   a(t)  \\cdot  \\dot X(t) +b(t)  \\cdot X(t)  + c(t)  \\cdot X^\\ast \\Big\\|_2^2\n' +
    '$$\n' +
    'let\n' +
    '$$\n' +
    'g(t) = a(t)  \\cdot  \\dot X(t) +b(t)  \\cdot X(t)  + c(t)  \\cdot X^\\ast\n' +
    '$$\n' +
    'then\n' +
    '\n' +
    '而 $\\forall \\ \\epsilon >0,\\quad \\exist \\ T > 0$ , (是否循环论证了？)\n' +
    '$$\n' +
    's.t. \\quad \\quad  \\forall \\  t>T , \\quad\n' +
    '\\|\\nabla F(X(s) ) \\|_q = \\| h(u_{\\lambda(t)})\\|_q\\leq t^{-m} \\cdot\n' +
    '\\Big( \\frac{q}{q-1}   \\|u_0\\|_2^2\\Big)^{1/q} \\cdot (1+\\epsilon)\n' +
    '$$\n' +
    'let $C= \\Big( \\frac{q}{q-1}   \\|u_0\\|_2^2\\Big)^{1/q} \\cdot (1+\\epsilon)$   , then \n'  
    
    
//

String.prototype.replaceAll = function(search, replacement) {
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};
function correct_dollar_symbol(page){ 
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  return  b.replaceAll( /D_O_A_L_A2_q_Time/g,  "$$$$") ;
 
}

